2008
DOI: 10.1088/1742-5468/2008/05/p05014
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Off-lattice radial Eden cluster growth in two and three dimensions

Abstract: An off-lattice Eden cluster growth model is introduced and implemented in two and three dimensions, using both a flat substrate with periodic boundary conditions and a radial geometry. Large-scale simulations are conducted to investigate the kinetic roughening. In the radial geometry, both the origin and center of mass are used to measure surface width, and growth exponent estimates in two dimensions verify previous findings that the choice of origin or center of mass does affect the growth exponent. The growt… Show more

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Cited by 11 publications
(19 citation statements)
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“…Off-lattice simulations of Eden clusters immersed in d = 2 dimensions confirmed the agreement with the KPZ growth exponent [4,7]. Recently, Kuennen and Wang [10] reported off-lattice simulations of radial Eden clusters in d = 3 dimensions, in which a growth exponent β ≈ 0.1, much smaller than the accepted KPZ value for flat substrates in 2+1 dimensions, β KP Z ≈ 0.24 [11], was observed.…”
supporting
confidence: 66%
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“…Off-lattice simulations of Eden clusters immersed in d = 2 dimensions confirmed the agreement with the KPZ growth exponent [4,7]. Recently, Kuennen and Wang [10] reported off-lattice simulations of radial Eden clusters in d = 3 dimensions, in which a growth exponent β ≈ 0.1, much smaller than the accepted KPZ value for flat substrates in 2+1 dimensions, β KP Z ≈ 0.24 [11], was observed.…”
supporting
confidence: 66%
“…It is worth noticing that the interface width in Eden B is very small (w < 2 lattice unities in figure 3 and w < 1.5 particle diameters in Ref. [10]), which hinders the observation of the asymptotic regime.…”
mentioning
confidence: 98%
“…In this section we derive for the first time the properties of the center-of mass fluctuations of the cluster interfaces described by radial stochastic growth equations. It was found numerically that the Eden center of mass fluctuates according to the power law C m ∼ t 2/5 in d = 1 + 1 [4], while in d = 2 + 1 there is a strong decrease in this exponent [46]. This reduced stochastic behavior in higher dimensions was predicted in [15] using radial growth equations, and here we examine further the compatibility among the equations and the Eden cluster dynamics.…”
Section: Center-of-mass Fluctuationsmentioning
confidence: 58%
“…The desired exponent is obtained for δ = 1 and Dt 0 = 2/5, however, this result is uniform in the spatial dimension and so cannot predict the (2 + 1)−dimensional behavior [46]. Additionally, this instability mechanism seems to be not well enough justified and too non-generic to be a good explanation of the observed phenomenology.…”
Section: Center-of-mass Fluctuationsmentioning
confidence: 84%
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